Continuous Non-malleable Codes

Non-malleable codes are a natural relaxation of error correcting/detecting codes that have useful applications in the context of tamper resilient cryptography. Informally, a code is non-malleable if an adversary trying to tamper with an encoding of a given message can only leave it unchanged or modify it to the encoding of a completely unrelated value. This paper introduces an extension of the standard non-malleability security notion – so-called continuous non-malleability – where we allow the adversary to tamper continuously with an encoding. This is in contrast to the standard notion of non-malleable codes where the adversary only is allowed to tamper a single time with an encoding. We show how to construct continuous non-malleable codes in the common split-state model where an encoding consist of two parts and the tampering can be arbitrary but has to be independent with both parts. Our main contributions are outlined below: 1. We propose a new uniqueness requirement of split-state codes which states that it is computationally hard to find two codewords C = (X0, X1) and C ′ = (X0, X ′ 1) such that both codwords are valid, but X0 is the same in both C and C ′. A simple attack shows that uniqueness is necessary to achieve continuous non-malleability in the split-state model. Moreover, we illustrate that non of the existing constructions satisfies our uniqueness property and hence is not secure in the continuous setting. 2. We construct a split-state code satisfying continuous non-malleability. Our scheme is based on the inner product function, collision-resistant hashing and non-interactive zero-knowledge proofs of knowledge and requires an untamperable common reference string. 3. We apply continuous non-malleable codes to protect arbitrary cryptographic primitives against tampering attacks. Previous applications of non-malleable codes in this setting required to perfectly erase the entire memory after each execution and and required the adversary to be restricted in memory. We show that continuous non-malleable codes avoid these restrictions.